scholarly journals Entropy and Geometric Objects

2017 ◽  
Author(s):  
Georg J. Schmitz
Keyword(s):  
Black Hole ◽  
Geometric Approach ◽  
Heaviside Function ◽  
Diffuse Interfaces ◽  
Positive Quantity ◽  
Final Formula ◽  
Geometric Objects ◽  
Statistical Sense ◽  
Function Definition ◽  
A Charge

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length LP—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

scholarly journals Self-force on a charge outside a five-dimensional black hole

2014 ◽  
Vol 89 (12) ◽  
Author(s):  
Matthew J. S. Beach ◽  
Eric Poisson ◽  
Bernhard G. Nickel
Keyword(s):  
Black Hole ◽  
Dimensional Black Hole ◽  
A Charge ◽  
Self Force

A geometric approach to the transpositional relations in dynamics of nonholonomic mechanical systems

2018 ◽  
Vol 15 (07) ◽  
pp. 1850112 ◽  
Author(s):  
Mahdi Khajeh Salehani
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Geometric Approach ◽  
Nonholonomic Mechanical Systems ◽  
Nonholonomic Dynamics ◽  
Geometric Objects

Exploring the geometry of mechanical systems subject to nonholonomic constraints and using various bundle and variational structures intrinsically present in the nonholonomic setting, we study the structure of the equations of motion in a way that aids the analysis and helps to isolate the important geometric objects that govern the motion of such systems. Furthermore, we show that considering different sets of transpositional relations corresponding to different transitivity choices provides different variational structures associated with nonholonomic dynamics, but the derived equations (being referred to as the generalized Hamel–Voronets equations) are equivalent to the Lagrange–d’Alembert equations. To illustrate results of this work and as some applications of the generalized Hamel–Voronets formalisms discussed in this paper, we conclude with considering the balanced Tennessee racer, as well as its modification being referred to as the generalized nonholonomic cart, and an [Formula: see text]-snake with three wheeled planar platforms whose snake-like motion is induced by shape variations of the system.

scholarly journals SUPERRADIANCE FROM A CHARGED DILATON BLACK HOLE

1992 ◽  
Vol 07 (37) ◽  
pp. 3449-3454 ◽  
Author(s):  
KIYOSHI SHIRAISHI
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Large Black Hole ◽  
Charge Loss ◽  
Klein Gordon ◽  
Dilaton Black Hole ◽  
A Charge

We study the behavior of the wave function of charged Klein-Gordon field around a charge dilaton black hole. The rate of spontaneous charge loss is estimated for large black hole case.

scholarly journals Supermassive black hole at the galactic center

2014 ◽  
Vol 12 (2) ◽  
pp. 201-210
Author(s):  
Alexander Zakharov
Keyword(s):  
Black Hole ◽  
Extra Dimensions ◽  
Galactic Center ◽  
Spot Size ◽  
Schwarzschild Black Hole ◽  
Naked Singularities ◽  
Supermassive Black Hole ◽  
Hole Charge ◽  
A Charge ◽  
Black Hole Solutions

We derive an analytical expression of a shadow size as a function of a charge in the Reissner - Nordstr?m (RN) metric. Using the derived expression we consider shadows for negative tidal charges and charges corresponding to naked singularities q=Q2/M2>1, where Q and M are black hole charge and mass, respectively. An introduction of a negative tidal charge q can describes black hole solutions in theories with extra dimensions, so following the approach we consider an opportunity to extend RN metric to negative Q2, while for the standard RN metric Q2 is always non-negative. We found that for q > 9=8 black hole shadows disappear. Significant tidal charges q=-6.4 are not consistent with observations of a minimal spot size at the Galactic Center observed in mm-band, moreover, these observations demonstrate that in comparison with the Schwarzschild black hole a Reissner-Nordstr?m black hole with a significant charge q ? 1 provides a better fit of recent observational data for the black hole at the Galactic Center.

scholarly journals Towards the black hole uniqueness: transverse deformations of the extremal Reissner-Nordström-(A)dS horizon

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Maciej Kolanowski
Keyword(s):  
Black Hole ◽  
Spherically Symmetric ◽  
Maxwell Theory ◽  
Finite Dimensional ◽  
A Charge

Abstract We study all transverse deformations of the extremal Reissner-Nordström–(A)dS horizon in the Einstein-Maxwell theory. No symmetry assumptions are needed. It is shown, that for the generic values of a charge, the only allowed deformation is spherically symmetric. However, it is shown that for fine-tuned values of the charge, the space of deformations is larger, yet still finite-dimensional.

scholarly journals Thermal interpretation of Schwinger effect in near-extremal RN black hole

2019 ◽  
Vol 28 (11) ◽  
pp. 1950139 ◽  
Author(s):  
Sang Pyo Kim ◽  
Hyun Kyu Lee ◽  
Yongsung Yoon
Keyword(s):  
Black Hole ◽  
Electric Field ◽  
Scalar Curvature ◽  
Effective Temperature ◽  
Effective Action ◽  
Coulomb Field ◽  
Schwinger Effect ◽  
The One ◽  
A Charge ◽  
Horizon Geometry

We propose a thermal interpretation of the Schwinger effect for charged spinless scalars and spin-1/2 fermions in an extremal and near-extremal Reissner–Nordström (RN) black hole. The emission of charges has the distribution with an effective temperature determined by the Davies–Unruh temperature for accelerating charges by the electric field and the scalar curvature of [Formula: see text] from the near-horizon geometry [Formula: see text]. We find a charge bound for the extremal micro-black hole to remain stable against the Schwinger emission in analogy with the Breitenlohner–Freedman bound for the [Formula: see text] space. In the in–out formalism, we find the one-loop QED effective action consistent with the vacuum persistence and interpret the vacuum persistence as the leading Schwinger effect and the effect of a charged vacuum of the Coulomb field.

scholarly journals Microscopic entropy of AdS3 black holes revisited

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Finn Larsen ◽  
Siyul Lee
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Entropy ◽  
Canonical Partition Function ◽  
Microscopic Description ◽  
Grand Canonical Partition Function ◽  
Ads Black Holes ◽  
Higher Dimensional ◽  
A Charge ◽  
Grand Canonical

Abstract We revisit the microscopic description of AdS3 black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS3/CFT2 correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is not respected by individual states. This interpretation provides a microscopic understanding of the hitherto mysterious charge constraints satisfied by all BPS black holes in AdS. We also develop thermodynamics and a nAttractor mechanism of AdS3 black holes in the nearBPS regime.

Enhanced Kozai–Lidov Eccentricity Oscillations in Nuclear Star Clusters

2021 ◽  
Vol 922 (1) ◽  
pp. 74
Author(s):  
Jaroslav Haas ◽  
Ladislav Šubr
Keyword(s):  
Black Hole ◽  
Large Scale ◽  
Galactic Nuclei ◽  
Orbital Elements ◽  
Eccentric Orbit ◽  
Massive Black Hole ◽  
First Order ◽  
Supermassive Black Hole ◽  
Statistical Sense ◽  
General Statistical

Abstract Stellar motions in the innermost parts of galactic nuclei, where the gravity of a supermassive black hole dominates, follow Keplerian ellipses to the first order of approximation. These orbits may be subject to periodic (Kozai–Lidov) oscillations of their orbital elements if some nonspherically distributed matter (e.g., a secondary massive black hole, coherent stellar subsystem, or large-scale gaseous structure) perturbs the gravity of the central supermassive black hole. These oscillations are, however, affected by the overall potential of the host nuclear star cluster. In this paper, we show that its influence strongly depends on the properties of the particular system, as well as the considered timescale. We demonstrate that for systems with astrophysically relevant parameters, the Kozai–Lidov oscillations of eccentricity can be enhanced by the extended potential of the cluster in terms of reaching significantly higher maximal values. In a more general statistical sense, the oscillations of eccentricity are typically damped. The efficiency of the damping, however, may be small to negligible for the suitable parameters of the system. This applies, in particular, in the case when the perturbing body is on an eccentric orbit.

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